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SplitIfs.lean
import Mathlib.Tactic.SplitIfs example (x : Nat) (p : Prop) [Decidable p] : x = if p then x else x := by split_ifs with h1 · rfl · rfl example (x y : Nat) (p : Prop) [Decidable p] (h : if p then x = y else y = x) : x = y := by split_ifs at h · exact h · exact h.symm example (x : Nat) (p q : Prop) [Decidab...
Inverses.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Group.Submonoid.Pointwise /-! # Submonoid of inverses Given a submonoid `N` of a monoid `M`, we define the submonoid `N.leftInv` as the submonoid ...
Power.lean
/- Copyright (c) 2014 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Ring.Int.Parity /-! # Results about powers in fields or...
Terminal.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal import Mathlib.CategoryTheory.Limits.HasLimits /-! # Initial and terminal objects in a category. ##...
Alg.lean
import Mathlib universe v u open CategoryTheory AlgCat set_option maxHeartbeats 10000 set_option synthInstance.maxHeartbeats 2000 variable (R : Type u) [CommRing R] /- We test if all the coercions and `map_add` lemmas trigger correctly. -/ example (X : Type u) [Ring X] [Algebra R X] : ⇑(𝟙 (of R X)) = id := by si...
Semisimple.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.Eigenspace.Basic import Mathlib.LinearAlgebra.Semisimple /-! # Eigenspaces of semisimple linear endomorphisms This file contains basic result...
Regular.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Dynamics.Ergodic.Action.Basic import Mathlib.MeasureTheory.Group.Prod /-! # Regular action of a group on itself is ergodic In this file we prove th...
Traversable.lean
import Mathlib.Tactic.DeriveTraversable import Mathlib.Control.Traversable.Instances set_option linter.style.commandStart false namespace Testing universe u structure MyStruct (α : Type) where y : ℤ deriving LawfulTraversable #guard_msgs (drop info) in #synth LawfulTraversable MyStruct inductive Either (α : T...
Pointwise.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Bounded import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Topology.MetricSpace.Thickening /-! # P...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
Category.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jingting Wang, Wanyi He, Nailin Guan -/ import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.RingTheory.QuotSMulTop /-! # Categorical constructions for `IsSMulRegular` -...
Sublattice.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.SupClosed /-! # Sublattices This file defines sublattices. ## TODO Subsemilattices, if people care about them. ## Tags sublattice -/ open Func...
extraspecial.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigop finset prime binomial. From mathc...
Cardinality.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.Data.Fintype.Pigeonhole import Mathlib.GroupTheory.OreLocalization.Basic import Mathlib.SetTheory.Cardinal.Arithmetic /-! # Cardinality of Ore localizations This fi...
Basic.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Defs import Mathlib.Data.Multiset.FinsetOps /-! # Lattice structure on finite sets T...
GammaSpecAdjunction.lean
/- Copyright (c) 2021 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.AlgebraicGeometry.Restrict import Mathlib.CategoryTheory.Adjunction.Limits import Mathlib.CategoryTheory.Adjunction.Opposites import Mathlib.CategoryTheory.Adjun...
Basic.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Yuyang Zhao -/ import Mathlib.Algebra.GroupWithZero.Units.Basic import Mathlib.Algebra.Notation.Pi.Defs import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs import M...
Comon_.lean
/- Copyright (c) 2023 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic import Mathlib.CategoryTheory.Monoidal.Comon_ /-! # Comonoid objects in a cartesian monoidal category. The catego...
Types.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.Satisfiability /-! # Type Spaces This file defines the space of complete types over a first-order theory. (Note that types in model theor...
Basic.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Exact import Mathlib.Algebra.Module.ULift import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.LinearAlgebra.Finsupp.LinearCombination /-! # Prese...
Inversion.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee, Óscar Álvarez -/ import Mathlib.GroupTheory.Coxeter.Length import Mathlib.Data.List.GetD import Mathlib.Tactic.Group /-! # Reflections, inversions, and inversion sequences...
Have.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino -/ import Mathlib.Tactic.Have example : Nat := by have h : Nat exact 5 exact h example : Nat := by have : Nat · exact 5 exact this example {a : Nat} : a =...
Defs.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Batteries.Data.Nat.Gcd import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Order.Group.Nat import Mathlib.Algebra.Order.Sub.Basic import Mathlib....
CotangentComplex.lean
import Mathlib.RingTheory.Extension.Cotangent.Basic deprecated_module (since := "2025-05-11")
mxpoly.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import div fintype tupl...
Slice.lean
/- Copyright (c) 2021 Bhavik Mehta, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies -/ import Mathlib.Data.Fintype.Powerset import Mathlib.Order.Antichain import Mathlib.Order.Interval.Finset.Nat import Mathlib.Alg...
Basic.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero /-! # Short complexes This file defines the category `ShortComplex C` of diagrams `X₁ ⟶ X₂ ⟶ X₃` such that the com...
Defs.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.Group.Nat.Hom import Mathlib.Algebra.Polynomial.Basic /-! # Evaluating a polynomial ## Main definit...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Order.Bounds.Image import Mathlib.Order.CompleteLattice.Basic import Mathlib.Order.WithBot /-! # Galois connections, insertions and coinsertions This...
Monoid.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot -/ import Mathlib.Algebra.Group.Basic import Mathlib.Data.Set.Function import Mathlib.Order.Interval.Set.Basic import Mathlib.Algebra.Order.Monoid.Defs...
Basic.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Interval.Set.Basic import Mathlib.Data.Set.Lattice.Image import Mathlib.Data.SetLike.Basic /-! # Order intervals This file defines (nonempty) close...
ContMDiffMFDeriv.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.MFDeriv.Tangent import Mathlib.Geometry.Manifold.ContMDiffMap import Mathlib.Geometry.Manifold.VectorBundle.H...
Equiv.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Data.FunLike.Embedding /-! # Typeclass for a type `F` with an injective map to `A ≃ B` This typeclass is primarily for use by isomorphisms like `MonoidEqui...
Embedding.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Logic.Embedding.Basic import Mathlib.Algebra.Group.Defs /-! # The embedding of a cancellative semigroup into itself by multiplication by a fixed element...
fintype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnotations eqtype. From mathcomp Require Import ssrnat seq choice pat...
NullSubmodule.lean
/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ import Mathlib.Analysis.Normed.Group.Continuity import Mathlib.Analysis.Normed.MulAction /-! # The null subgroup in a seminormed commutative group For any `SeminormedAd...
Units.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl -/ import Mathlib.Order.Hom.Basic import Mathlib.Order.MinMax import Mathlib.Algebra.Group.Units.Defs /-! # Units in or...
PathConnected.lean
/- Copyright (c) 2020 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Topology.Path /-! # Path connectedness Continuing from `Mathlib/Topology/Path.lean`, this file defines path components and path-connected spaces. ##...
Estimator.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Data.List.EditDistance.Bounds import Mathlib.Order.Estimator /-! # `Estimator` for Levenshtein distance. The usual algorithm for computing Levenshtein di...
ContinuousLinearMap.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual import Mathlib.MeasureTheory.Integral.Bochner.Set import Mathlib.Topology.ContinuousMap.C...
Support.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set import Mathlib.Algebra.Notation.Support /-! # Support of a function composed with a scalar action We...
Basic.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Polynomial.Splits import Mathlib.FieldTheory.RatFunc.AsPolynomial import Mathlib.NumberTheory.ArithmeticFunction import Mathlib.RingTheory.Ro...
deriving_countable.lean
import Mathlib.Tactic.DeriveCountable import Mathlib.Data.Countable.Basic import Mathlib.Logic.Equiv.List /-! # Tests of the `Countable` deriving handler -/ namespace Test /-! Structure -/ structure S (α β : Type*) where x : α y : List β deriving Countable example : Countable (S Nat Bool) := inferInstance /-...
Basic.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov, Yakov Pechersky -/ import Mathlib.Algebra.Group.Subsemigroup.Defs import M...
HashCommandLinter.lean
import Lean.Elab.GuardMsgs import Mathlib.Tactic.AdaptationNote import Mathlib.Tactic.Linter.HashCommandLinter set_option linter.hashCommand true section ignored_commands -- As a consequence of https://github.com/leanprover/lean4/pull/5644, `#guard_msgs in`, even without a doc-string, -- does not triggers the `#`-co...
closed_field.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype generic_...
MulAction.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Data.ENNReal.Action import Mathlib.Topology.Algebra.UniformMulAction import Mathlib.Topology.MetricSpace.Algebra ...
PrimePow.lean
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Algebra.IsPrimePow import Mathlib.Data.Nat.Factorization.Basic import Mathlib.Data.Nat.Prime.Pow import Mathlib.NumberTheory.Divisors /-! # Prime powers a...
Basic.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplexCategory.Defs import Mathlib.Data.Fintype.Sort import Mathlib.Order.Category.NonemptyFinLin...
Reverse.lean
/- Copyright (c) 2020 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Polynomial.Degree.TrailingDegree import Mathlib.Algebra.Polynomial.EraseLead /-! # Reverse of a univariate polynomial The main definition is `r...
PhragmenLindelof.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Complex.AbsMax import Mathlib.Analysis.Asymptotics.SuperpolynomialDecay /-! # Phragmen-Lindelöf principle In this file we prove several ve...
Lex.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Junyan Xu -/ import Mathlib.Algebra.Order.Group.PiLex import Mathlib.Data.DFinsupp.Order import Mathlib.Data.DFinsupp.NeLocus import Mathlib.Order.WellFoundedSet /-! # Lexic...
DecisionNec.lean
/- Copyright (c) 2020 Gihan Marasingha. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gihan Marasingha -/ import Archive.MiuLanguage.Basic import Mathlib.Data.List.Basic import Mathlib.Data.Nat.ModEq /-! # Decision procedure: necessary condition We introduce a condi...
Triangle.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Manuel Candales -/ import Mathlib.Geometry.Euclidean.Angle.Oriented.Affine import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine import Mathlib.Tactic.IntervalCases /-...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
Polar.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Kalle Kytölä -/ import Mathlib.Analysis.Normed.Module.Basic import Mathlib.LinearAlgebra.SesquilinearForm import Mathlib.Topology.Algebra.Module.WeakBilin /-! # Polar set I...
Torsion.lean
/- Copyright (c) 2025 Yaël Dillies, Patrick Luo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Patrick Luo -/ import Mathlib.Algebra.Group.Basic import Mathlib.Tactic.MkIffOfInductiveProp /-! # Torsion-free monoids and groups This file defines torsion-...
Triangle.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Triangulated.Basic import Mathlib.CategoryTheory.Triangulated.Opposite.Basic /-! # Triangles in the opposite category of a (pre)triangulated cate...
Over.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Sites.CoverLifting import Mathlib.CategoryTheory.Sites.CoverPreserving /-! Localization In this file, given a Grothendieck topology `J` on a cat...
Indicator.lean
/- Copyright (c) 2023 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable import Mathlib.MeasureTheory.Integral.Lebesgue.DominatedConvergence /-! # Results about indicator functi...
presentation.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq. From mathcomp Require Import fintype finset fingroup morphism. (**********************...
Bertrand.lean
/- Copyright (c) 2020 Patrick Stevens. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Stevens, Bolton Bailey -/ import Mathlib.Data.Nat.Choose.Factorization import Mathlib.NumberTheory.Primorial import Mathlib.Analysis.Convex.SpecificFunctions.Basic import Math...
Real.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Topology.Connected.PathConnected import Mathlib.Topology.Instances.AddCircle.Defs import Mathlib.Topology.Instances.ZMultiples /-! # The additive circle ove...
SimplicialObject.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialObject.Basic import Mathlib.CategoryTheory.Idempotents.FunctorCategories /-! # Idempotent completeness of categories of simplicial ...
WithTop.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Ring.Nat import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop /-! # Lemma about the coercion `ℕ → WithBot ℕ`. An orphaned lemma about castin...
OfAssociative.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.Basic import Mathlib.Algebra.Lie.Subalgebra import Mathlib.Algebra.Lie.Submodule import Mathlib.Algebra.Algebra.Subalgebra.Basic /-! # Lie algeb...
Basic.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.GroupWithZero.NeZero import Mathlib.Logic.Unique import Mathlib.Tactic.Conv /-! # Groups with an adjoined z...
Defs.lean
/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.Data.List.Defs import Mathlib.Tactic.Common /-! The type `List.Vector` represents lists with fixed length. TODO: The API of `List.Vector` i...
BochnerL1.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner.L1 deprecated_module (since := "2025-04-06")
IsomOfJ.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms import Mathlib.FieldTheory.IsSepClosed /-! # Elliptic curves with same j-invariants are isomorphic ## Main results - `W...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
Bounds.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Order.Group.OrderIso import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual import Mathlib.Order.Bounds.OrderIso import Mathlib.Order.Galois...
Symmetric.lean
/- Copyright (c) 2021 Lu-Ming Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lu-Ming Zhang -/ import Mathlib.Data.Matrix.Basic import Mathlib.Data.Matrix.Block /-! # Symmetric matrices This file contains the definition and basic results about symmetric matrice...
Rat.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Order.Group.Unbundled.Basic import Mathlib.Algebra.Ring.Rat import Mathlib.Dat...
Bipartite.lean
/- Copyright (c) 2025 Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Horner -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Combinatorics.Enumerative.DoubleCounting import Mathlib.Combinatorics.SimpleGraph.Coloring import Mathlib.C...
Function.lean
/- Copyright (c) 2019 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, François Dupuis -/ import Mathlib.Analysis.Convex.Basic import Mathlib.Order.Filter.Extr import Mathlib.Tactic.NormNum /-! # Convex and concave functions This...
Lattice.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Algebra.Order.Group.PosPart import Mathlib.MeasureTheory.Group.Arithmetic import Mathlib.MeasureTheory.Order.Lattice /-! # Measurability results on grou...
Separation.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.Topology.Separation.Hausdorff import Mathlib.Topology.Connected.TotallyDisconnected /-! # Separation and (dis)connectedness properties of topologi...
Diagonal.lean
/- Copyright (c) 2018 Ellen Arlt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang -/ import Mathlib.Data.Int.Cast.Basic import Mathlib.Data.Int.Cast.Pi import Mathlib.Data.Matrix.Defs imp...
Coevaluation.lean
/- Copyright (c) 2021 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.LinearAlgebra.Contraction /-! # The coevaluation map on finite dimensional vector spaces Given a finite dimensional vector space `V` over a field...
Prod.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.LpSeminorm.Basic import Mathlib.MeasureTheory.Measure.Prod /-! # ℒp spaces and products -/ open scoped ENNReal namespace Measur...
SeparableClosure.lean
/- Copyright (c) 2023 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.FieldTheory.SeparableDegree import Mathlib.FieldTheory.IsSepClosed /-! # Separable closure This file contains basics about the (relative) separable closure of a fie...
Lex.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.GroupWithZero.ProdHom import Mathlib.Algebra.Order.Group.Equiv import Mathlib.Algebra.Order.Monoid.Lex import Mathlib.Algebra.Order.Hom.Monoi...
SeparableMeasure.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.MeasureTheory.Function.SimpleFuncDenseLp import Mathlib.MeasureTheory.SetAlgebra /-! # Separable measure The goal of this file is to give a sufficien...
InducedCategory.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Reid Barton -/ import Mathlib.CategoryTheory.Functor.FullyFaithful /-! # Induced categories and full subcategories Given a category `D` and a function `F : C → D `from a ...
Imo2024Q2.lean
/- Copyright (c) 2024 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.FieldTheory.Finite.Basic /-! # IMO 2024 Q2 Determine all pairs $(a,b)$ of positive integers for which there exist positive integers $g$ and $N$ such that...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
KleinFour.lean
/- Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer import Mathlib.GroupTheory.SpecificGroups.KleinFour import Mathlib.GroupTheory.Sylow ...
TerminatedStable.lean
/- Copyright (c) 2020 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Translations /-! # Stabilisation of gcf Computations Under Termination ## Summary We show that the continuants and co...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
ContinuousEvalConst.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Constructions /-! # Bundled morphisms with continuous evaluation at a point In this file we define a typeclass saying that `F` is a type o...
TypeCheck.lean
import Mathlib.Tactic.TypeCheck set_option linter.unusedTactic false /-- A term where `inferType` returns `Prop`, but which does not type check. -/ elab "wrong" : term => return Lean.mkApp2 (.const ``id [.zero]) (.sort .zero) (.app (.sort .zero) (.sort .zero)) /-- info: Type --- info: Bool --- info: Nat --- info: ...
UnderlyingMap.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Topology.LocalAtTarget import Mathlib.AlgebraicGeometry.Morphisms.Constructors /-! ## Properties on the underlying functions of morphisms of schemes. This...
quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype prim...
EnoughProjectives.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences /-! # Smallness of Ext-groups from the existence of enough projectives Let `C : Type u` be an abelian categ...
Associator.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.GradedObject.Trifunctor /-! # The associator for actions of bifunctors on graded objects Given functors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂`, `G : C₁₂ ⥤ C₃ ⥤ C...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
GromovHausdorffRealized.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli import Mathlib.Topology.ContinuousMap.Bounded.Normed import Mathlib.Topology.MetricSpace.Gluing impor...
LeftRight.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Order.Antichain import Mathlib.Topology.ContinuousOn /-! # Left and right continuity In this file we prove a few lemmas about left and right cont...
finmodule.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...